Multiplication property

Definition

The multiplication property of equality states that you can multiply both sides of an equation by the same non-zero number without changing the equation's solutions. It is a fundamental principle used to solve equations and inequalities.

5 Must Know Facts For Your Next Test

1. If $a = b$, then $ac = bc$ for any non-zero number $c$.
2. Multiplying both sides of an inequality by a positive number preserves the inequality's direction.
3. Multiplying both sides of an inequality by a negative number reverses the inequality's direction.
4. The multiplication property is essential for isolating variables in linear equations and inequalities.
5. This property also applies to absolute value inequalities when considering different cases (positive and negative).

Review Questions

• What happens to an inequality when you multiply both sides by a negative number?
• How would you isolate the variable in the equation $3x = 12$ using the multiplication property?
• When solving $|x - 5| < 10$, how can the multiplication property be applied?

Related terms

Addition Property of Equality: States that adding the same number to both sides of an equation does not change its solutions.

Division Property of Inequality: States that dividing both sides of an inequality by a positive number preserves its direction, but dividing by a negative number reverses it.

Absolute Value Inequality: An inequality that involves absolute values, often requiring consideration of two separate cases.